$A$ $B$ $C$ If: $ BC = 6x + 5$, $ AC = 98$, and $ AB = 8x + 9$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 9} + {6x + 5} = {98}$ Combine like terms: $ 14x + 14 = {98}$ Subtract $14$ from both sides: $ 14x = 84$ Divide both sides by $14$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 6({6}) + 5$ Simplify: $ {BC = 36 + 5}$ Simplify to find ${BC}$ : $ {BC = 41}$